Evaluate the following definite integral
$integral subscript 0 superscript 8 straight x to the power of 5 over 3 end exponent dx$

Solution

Let I = $integral subscript 0 superscript 8 straight x to the power of 5 over 3 end exponent space dx space minus space open square brackets fraction numerator straight x to the power of begin display style 8 over 3 end style end exponent over denominator begin display style 8 over 3 end style end fraction close square brackets subscript 0 superscript 8 space equals space 3 over 8 open square brackets straight x to the power of 8 over 3 end exponent close square brackets subscript 0 superscript 8$
$equals space 3 over 8 open square brackets left parenthesis 8 right parenthesis to the power of 8 over 3 end exponent minus 0 close square brackets space equals space 3 over 8 left parenthesis 2 to the power of 8 minus 0 right parenthesis space equals space 3 over 8 cross times 256 space equals space 96$

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Integrals

Evaluate the following definite integral
$integral subscript 0 superscript 8 straight x to the power of 5 over 3 end exponent dx$

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